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News & Stories: 2009-10

Interim 2010: Modal Logic
January 29, 2010

“Let no one ignorant of modal logic enter here.”

Tradition states that above the entrance to Plato’s Academy were inscribed the words, “Let no one ignorant of geometry enter here.”

Student writing modal logic equations on the board
A student in the modal logic interim course studies how subjunctives compare with conditional probabilities in probability theory.

Tomis Kapitan, Presidential Teaching Professor in the philosophy department at Northern Illinois University, says he might modify that statement to read: "Let no one enter graduate school in philosophy who has not studied modal logic."

Most philosophy students study advanced topics like modal logic for the first time in graduate school. But it’s to the student’s advantage to be exposed to modal logic as undergraduates, says Calvin professor Stephen Wykstra. However, an advanced field of logic like modality rarely fits into an undergraduate philosophical curriculum.

Interim focus

Calvin’s January term has given Wykstra an opportunity to teach "Modal Logic: Theory and Applications" for the past two years. Last year, six senior philosophy majors, all headed to graduate school, petitioned Wykstra to teach the course. "So it was sort of our ‘send-off present’ for them,” says Wykstra. “But it’s also an opportunity for me to become more familiar with modal logic. I think that’s part of the interim ideal; a professor can push into a place he or she isn’t entirely familiar with, and students and professor can learn together.”

The subject matter is difficult, admits Wystra. But he also says that students shouldn’t be intimidated by it. “It doesn’t always come easy for me,” says Wykstra. “You have to work to be comfortable with it.”

"It’s been pretty hard,” confirms sophomore Aaron Franklin. “It’s hard to learn all the new terms, and how they relate.” His classmates concur: learning the language of modal logic has certainly not been easy. But despite the difficulty, Professor Wykstra has made the material accessible, says junior Cameron Gibbs.

Modal logic at work

The class consists of a “formal logic” layer and an “application” layer—the latter of which shows students how contemporary philosophers apply the tools of modality to philosophical problems. This month the class has been using the evidential problem of evil as its primary “case study” for how modal concepts can inform a contemporary philosophical debate.

Lu Teng, an exchange student from Wuhan University in China, says, "In China I studied a lot of logic, and a lot of logic that was very hard. But it was more like studying mathematics—I never was sure what it related to. Here I see the applications from Professor Wykstra.”

"One of the foibles of advanced logic is that it can seem tedious and uninteresting at times,” says senior Tim Perrine. “But in this class I knew I was gaining a tool that I could apply, and that would be fruitful for future use.”

Students in the modal logic interim course work out equations on the blackboard

Senior philosophy major Emi Okayasu explains an element of modal logic to classmates Lu Teng and Quan Jin. Teng and Jin are both visiting students in Calvin's philosophy department from Wuhan University in China.

Philosophy as a living discipline

The application portion of the class also provides students with front-row seats to living debates within philosophy—what arguments and counterarguments are being presented in the field right now. This year’s modal logic students even have an opportunity to read and respond to a paper co-authored by Wykstra and one of their classmates, Tim Perrine. The paper will be presented at the Pacific Division meeting of the American Philosophical Association this spring.

"Once nice thing about the class is that there was a real sense of community and teamwork,” says Perrine. ”And since this is a current research interest of Professor Wykstra’s, there really was a sense of the professor and the students getting together in a circle and trying to understand particular ideas and how they fit. That’s a nice feeling for a class that you don’t get very often.”

"Studying modal logic has allowed me to study the places where philosophy intersects with topics in other departments,” says senior Emi Okayasu. “It’s shown me that philosophy is not just the history of thought…it’s a very dynamic discipline.” Quan Jin, also visiting from Wuhan University, adds, “It’s shown me that analytic philosophy isn’t trivial.”

Wykstra says that his goal is to give students exposure to theories of modal logic. “I want them to have the basic language down…[and] to have the street smarts to enter into a discussion and not feel lost,” he says. “I don’t expect them to become like tai chi masters who know all the right moves… I just want them to be able to handle themselves in a street brawl.”

~by Ashleigh Draft, communications and marketing

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What is modal logic?

A fundamental tool of contemporary analytic philosophy

Modal logic is a specialized branch of modern symbolic logic. It studies the rules governing inferences that rely on “modal” concepts like necessity and possibility, and many others. Also it studies the logic of inferences involving so-called “subjunctive” (or "counterfactual”) conditionals, which obey different rules than do “straight” conditionals. In David Lewis' well-known example, “IF Oswald did not shoot Kennedy, then someone else did” is pretty clearly a true proposition; but “IF Oswald were not to have shot Kennedy, someone else would have” is not. Modal concerns enter centrally into disputes about free will and responsibility, causation, the problem of evil and epistemology. 

~Steven Wykstra, professor of philosophy

More on modal logic »